Dynamics of a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation

[+] Author and Article Information
Kazuyuki Yagasaki

Department of Mechanical Engineering, Tamagawa University, Machida, Tokyo 194, Japan

Masaru Sakata, Koji Kimura

Department of Mechanical Engineering Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152, Japan

J. Appl. Mech 57(1), 209-217 (Mar 01, 1990) (9 pages) doi:10.1115/1.2888306 History: Received August 23, 1988; Revised March 27, 1989; Online March 31, 2008


In this paper we study the dynamics of a weakly nonlinear single-degree-of-freedom system subjected to combined parametric and external excitation. The averaging method is used to establish the existence of invariant tori and analyze their stability. Furthermore, by applying the Melnikov technique to the average system it is shown that there exist transverse homoclinic orbits resulting in chaotic dynamics. Numerical simulation results are also given to demonstrate the theoretical results.

Copyright © 1990 by The American Society of Mechanical Engineers
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